The performance of speaker identification (SID) systems can be improved by the addition of the rapidly varying "fine structure" features of formant amplitude and/or frequency modulation and multiple excitation pulses. This paper shows how the estimation of such fine structure features can be improved further by obtaining better estimates of formant frequency locations and uncovering various sources of error in the feature extraction systems. Most female telephone speech showed "spurious" formants, due to distortion in the telephone network. Nevertheless, SID performance was greatest with these spurious formants as formant estimates. A new feature has also been identified which can increase SID performance: cepstral coefficients from noise in the estimated excitation waveform. Finally, statistical tools have been developed to explore the relative importance of features used for SID, with the ultimate goal of uncovering the source of the features that provide SID performance improvement.